"It is quite conceivable that an instrument could be built that would be capable of an automatic change of pitch throughout its entire range, up or down by any reasonable interval, and if Just Intonation can surmount the many hazards and problems ... the problem of transposition may be considered minor, one for which a solution will inevitably be found."

Rationale: Music That Has Never Existed

Rationale is a free, open-source music sequencing program designed specifically for the extended just intonation tuning system.

There are a few aspects of Rationale that are pretty unusual, in order to relate these esoteric intervals to something concrete without too many big numbers.

One of Partch's ideas was that the just tonal center needn't be any more fixed than that of traditional Western 12-tone theory. In fact, if you consider that any available tone could be at the center of a tonality change (or key change), then there ought to be far more possibilities with a just tuning system than with a tempered scale. It's just hard to realize this with 12 notes or less, which leads many people to say you can't perform key changes freely in just intonation. Partch's famous 43-tone octave (he winced at both the word "note" and the word "scale") came about from the necessity to have available enough tones to create a sense of tonality around any of the more important tones: for instance, if you modulate to a 7/5 O-tonality, you need to represent the 3rd harmonic in that tonality, meaning something like 21/20. Unfortunately, if you want to perform the same modulation from there, thus 7/5 * 7/5, or 49/25, then the 3rd harmonic will be 147/100, a ratio that doesn't mean much intuitively. Rationale is my attempt to solve this problem.

Rationale is available at Sourceforge. It requires Python 2.5 and the Csound Python API (installed as csnd.py), both of which are available free online.